This paper presents ReproRun, a flexible and extensible run-time framework for the reconfiguration of functions in field programmable gate array (FPGA) devices used in popular software-defined radio (SDR) platforms. The FPGA devices embed a hardwired or soft processing system (PS) which communicates with the programmable logic (PL) using a standard embedded bus interface. In order to apply a seamless run-time partial reconfiguration, we made use of all the related building blocks, design guidelines, and tools offered by AMD-Xilinx. In ReproRun, each partial bitstream targeting a reconfigurable region (RR) of the PL area comes with its respective firmware (i.e., software functions) that runs on the PS side. Our work guarantees run-time updates of the firmware without interrupting the functionality of other software processes running in the PS or PL, by employing a specialized controller, denoted as Run-timE firmWare reconfIguration contRollEr (REWIRE). The latter leverages the open asymmetric multiprocessing framework (OpenAMP). The partial bitstreams and respective firmware are fetched from a remote location using the trivial file transfer protocol (TFTP). ReproRun can be applied in different FPGA accelerators residing in disaggregated open radio access network (RAN) equipment, adaptive radio access technologies, and Edge servers hosting virtualized functions.